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What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units

2 Answers

3 votes

Answer:

C

Explanation:

User Panther
by
8.5k points
2 votes

Answer:


√(85).

Explanation:


x-coordinates:

  • First point:
    -1.
  • Second point:
    6.
  • Difference:
    |-1 - 6| = |-7| = 7.


y-coordinates:

  • First point:
    4.
  • Second point:
    -2.
  • Difference:
    |4 - (-2)| = |6| = 6.

Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:

  • the difference between the two
    x-coordinates,
    7, and
  • the difference between the two
    y-coordinates,
    6.

Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)


\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= √(7^2 + 6^2) \\ &= √(85)\end{aligned}.

What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square-example-1
User Juan Rodriguez
by
8.0k points

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